This is one of the more surprising responses but also one of the more interesting.
What is the long term impact on Russia and Central Asia? Is Muscovite expansion in *all* directions aided, or only to the south and east?
My opinion is that without Timur, the Golden Horde would fair worse. It was Timur that assisted and tutored the younger Tokhtamush and favored the Golden Horde, initially. This allowed the phenomenal leader and warrior Tokhtamush to become ruler of the Tartars and under his reign, prior to the break between he and Timur, defeated various resurgent Slavic states, especially Muscovy. Without Timur, he likely never takes the throne and Muscovite expansion south and east begins earlier with the Golden Horde dealt substantial blows.
The only option is that Tokhtamush seeks refuge in the Ottoman court. This is one option for his survival, but equally unlikely as Timur’s assistance.
Interesting point of view with which I happened to disagree. Internal squabbles in the Golden Horde were a routine thing but eventually Timur almost completely destroyed it as a "civilization": it was in a process of interesting and rather unpredictable evolution from a nomadic state to at least semi-sedentary one and Timur interrupted this process by destroying its economy to such a degree that it could never get back. Not to mention that he pretty much cut off the existing trade routes supporting the Horde's economy making its breakdown just a matter of time.
As for Tokhtamush, his elevation into something "phenomenal" (except for the phenomenal ability of self-destruction and phenomenal absence of comprehension) is something completely new to me.
Regarding defeat of the "resurgent" Moscow, this is a "cultural misunderstanding". Moscow rebelled against emir Mamai and presumably defeated him in a battle (it seems that now almost all facts related to this event are being questioned, staring from its scope and all the way to geography). From Tokhtamush's (and everybody else) perspective Mamai was an usurper because he was not a Genghizid. So, based upon a "common sense" logic, the prince of Moscow did Tokhtamush a favor. But this type of a logic does not apply because a rule was that the subjects must not interfere into the affairs of their rulers (at some point Timur executed leaders of his city who in his absence repelled attack of his enemy without his order). Mamai could be an usurper but he represented (illegally but still) the Golden Horde and Prince Dmitri was a rebellious subject. Dealing with Mamai was Tokhtamush's business, not Dmitri's. It seems that the issue was well understood by both sides because Dmitri fled from Moscow when Tokhtamush approached. But "phenomenal warrior" failed to take it by storm. He had to offer an amnesty and then execute the delegation of the city leaders and use state of a resulting anarchy to get into it.
Absence of Tokhtamush would mean either revenge by Mamai (he was gathering a new army when Tokhtamush attacked him) or accession of another Genghizid but generally stronger Horde would prevent earlier expansion of Moscow. Actually, such an expansion would not happen anyway because the really growing and expanding regional power at that time was Lithuania: it included more "Russian" lands that Princedom of Moscow and controlled even more in a loose dependency. Witold ended up as "protector" of Princedom of Moscow.
Actually, besides the Ottoman option (pretty much useless in the terms of comeback), there was a quite realistic Lithuanian one, which Tokhtamush used later: he fled to Grand Duke Witold and made an agreement according to which he, as a reward for his restoration, will become Witold's vassal and transfer to him sovereignty over the Russian princedoms.